x=(50000-x)*(10/7)

Solution for x=(50000-x)*(10/7) equation:

x=(50000-x)(10/7)

We move all terms to the left:

x-((50000-x)(10/7))=0

We add all the numbers together, and all the variables

x-((-1x+50000)(+10/7))=0

We multiply parentheses ..

-((-10x^2+50000*10/7))+x=0

We multiply all the terms by the denominator


-((-10x^2+50000*10+x*7))=0


We calculate terms in parentheses: -((-10x^2+50000*10+x*7)), so:

(-10x^2+50000*10+x*7)

We get rid of parentheses

-10x^2+x*7+50000*10

We add all the numbers together, and all the variables

-10x^2+x*7+500000

Wy multiply elements

-10x^2+7x+500000

Back to the equation:

-(-10x^2+7x+500000)


We get rid of parentheses

10x^2-7x-500000=0

a = 10; b = -7; c = -500000;
Δ = b2-4ac
Δ = -72-4·10·(-500000)
Δ = 20000049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{20000049}}{2*10}=\frac{7-\sqrt{20000049}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{20000049}}{2*10}=\frac{7+\sqrt{20000049}}{20}
$